arXiv subjects
Publications and source records attributed to Chunhui Liu.
In this paper, we will give an upper bound of the number of auxiliary hypersurfaces in the determinant method, which reformulates an unpublished work of Salberger by Arakelov geometry. One of the key constants will be determined by the pseudo-effective threshold of certain line bundles.
In this paper, for a geometrically integral projective scheme, we will give an upper bound of the product of the norms of its non-geometrically integral reductions over an arbitrary number field. For this aim, we take the adelic viewpoint on this subject.
For a reduced projective scheme over the ring of integers of a number field, the set of places over which the fibres of the scheme are not reduced is a finite set. We give an explicit upper bound for the product of the norms of places in this set. For this purpose, we introduce a generalization of the notion of height over the adelic ring. We reduce the general case of a scheme of pure dimension to the case of a hypersurface by using the theory of Chow varieties. The case of a hypersurface is then treated with the help of the resultant of the equation of the hypersurface with some partial derivatives of the equation.
In the world of action recognition research, one primary focus has been on how to construct and train networks to model the spatial-temporal volume of an input video. These methods typically uniformly sample a segment of an input clip (along the temporal dimension). However, not all parts of a video are equally important to determine the action in the clip. In this work, we focus instead on learning where to extract features, so as to focus on the most informative parts of the video. We propose a method called the non-uniform temporal aggregation (NUTA), which aggregates features only from informative temporal segments. We also introduce a synchronization method that allows our NUTA features to be temporally aligned with traditional uniformly sampled video features, so that both local and clip-level features can be combined. Our model has achieved state-of-the-art performance on four widely used large-scale action-recognition datasets (Kinetics400, Kinetics700, Something-something V2 and Charades). In addition, we have created a visualization to illustrate how the proposed NUTA method selects only the most relevant parts of a video clip.
Video action recognition is one of the representative tasks for video understanding. Over the last decade, we have witnessed great advancements in video action recognition thanks to the emergence of deep learning. But we also encountered new challenges, including modeling long-range temporal information in videos, high computation costs, and incomparable results due to datasets and evaluation protocol variances. In this paper, we provide a comprehensive survey of over 200 existing papers on deep learning for video action recognition. We first introduce the 17 video action recognition datasets that influenced the design of models. Then we present video action recognition models in chronological order: starting with early attempts at adapting deep learning, then to the two-stream networks, followed by the adoption of 3D convolutional kernels, and finally to the recent compute-efficient models. In addition, we benchmark popular methods on several representative datasets and release code for reproducibility. In the end, we discuss open problems and shed light on opportunities for video action recognition to facilitate new research ideas.
Mining the shared features of same identity in different scene, and the unique features of different identity in same scene, are most significant challenges in the field of person re-identification (ReID). Online Instance Matching (OIM) loss function and Triplet loss function are main methods for person ReID. Unfortunately, both of them have drawbacks. OIM loss treats all samples equally and puts no emphasis on hard samples. Triplet loss processes batch construction in a complicated and fussy way and converges slowly. For these problems, we propose a Triplet Online Instance Matching (TOIM) loss function, which lays emphasis on the hard samples and improves the accuracy of person ReID effectively. It combines the advantages of OIM loss and Triplet loss and simplifies the process of batch construction, which leads to a more rapid convergence. It can be trained on-line when handle the joint detection and identification task. To validate our loss function, we collect and annotate a large-scale benchmark dataset (UESTC-PR) based on images taken from surveillance cameras, which contains 499 identities and 60,437 images. We evaluated our proposed loss function on Duke, Marker-1501 and UESTC-PR using ResNet-50, and the result shows that our proposed loss function outperforms the baseline methods by a maximum of 21.7%, including Softmax loss, OIM loss and Triplet loss.
We present compositional nearest neighbors (CompNN), a simple approach to visually interpreting distributed representations learned by a convolutional neural network (CNN) for pixel-level tasks (e.g., image synthesis and segmentation). It does so by reconstructing both a CNN's input and output image by copy-pasting corresponding patches from the training set with similar feature embeddings. To do so efficiently, it makes of a patch-match-based algorithm that exploits the fact that the patch representations learned by a CNN for pixel level tasks vary smoothly. Finally, we show that CompNN can be used to establish semantic correspondences between two images and control properties of the output image by modifying the images contained in the training set. We present qualitative and quantitative experiments for semantic segmentation and image-to-image translation that demonstrate that CompNN is a good tool for interpreting the embeddings learned by pixel-level CNNs.
In this paper, we will give an upper bound and a lower bound of the arithmetic Hilbert-Samuel function of projective hypersurfaces, which are uniform and explicit. These two bounds have the optimal dominant terms. As an application, we use the lower bound to get an estimate of the density of rational points with small heights in a hypersurface.
We fix a counting function of multiplicities of algebraic points in a projective hypersurface over a number field, and take the sum over all algebraic points of bounded height and fixed degree. An upper bound for the sum with respect to this counting function will be given in terms of the degree of the hypersurface, the dimension of the singular locus, the upper bounds of height, and the degree of the field of definition.
Despite the fact that many 3D human activity benchmarks being proposed, most existing action datasets focus on the action recognition tasks for the segmented videos. There is a lack of standard large-scale benchmarks, especially for current popular data-hungry deep learning based methods. In this paper, we introduce a new large scale benchmark (PKU-MMD) for continuous multi-modality 3D human action understanding and cover a wide range of complex human activities with well annotated information. PKU-MMD contains 1076 long video sequences in 51 action categories, performed by 66 subjects in three camera views. It contains almost 20,000 action instances and 5.4 million frames in total. Our dataset also provides multi-modality data sources, including RGB, depth, Infrared Radiation and Skeleton. With different modalities, we conduct extensive experiments on our dataset in terms of two scenarios and evaluate different methods by various metrics, including a new proposed evaluation protocol 2D-AP. We believe this large-scale dataset will benefit future researches on action detection for the community.
In this paper, we consider a problem of counting multiplicities. We fix a counting function of multiplicity of rational points in a hypersurface of a projective space over a finite field, and we give an upper bound for the sum with respect to this counting function in terms of the degree of the hypersurface, the dimension and the cardinality of the finite field. This upper bound gives a description of the complexity of the singular locus of this hypersurface. In order to obtain this upper bound, we introduce a notion called intersection tree by intersection theory. We construct a sequence of intersections, such that the multiplicity of a singular rational point is equal to that of one of the irreducible components in these intersections. The multiplicities of these irreducible components constructed above are bounded by their multiplicities in the intersection tree.